Grateful thanks to MJR and Steve for pointing me in the right direction over my DOS <-> Linux ethernet link. After some Googling, I found something called XFS for DOS V1.86, which appears to provide the DOS end of NFS, so presumably if I can get that to work then I can use NFS at the Linux end. XFS seems quite old (c. 1994) and the documentation leaves a huge amount to be desired, but if it does the job, I suppose I can't complain!
For now, I'm trying desperately hard to learn about networking on the Linux end. (Not trivial for a Bear of Little Brain....) The plan is to get the two machines to respond to the 'ping' function first and then (hopefully) progress from there.
If anyone's interested, I could report back when I've finally got it to go. Thanks again for the pointers!
Gerald.